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宝宝包包 · 2020年02月05日

问一道题:NO.PZ2019103001000033

问题如下:

Doug Kepler, the newly hired chief financial officer for the City of Radford, asks the deputy financial manager, Hui Ng, to prepare an analysis of the current investment portfolio and the city’s current and future obligations. The city has multiple liabilities of different amounts and maturities relating to the pension fund, infrastructure repairs, and various other obligations.

Ng observes that the current fixed-income portfolio is structured to match the duration of each liability. Previously, this structure caused the city to access a line of credit for temporary mismatches resulting from changes in the term structure of interest rates

Kepler asks Ng for different strategies to manage the interest rate risk of the city’s fixed-income investment portfolio against one-time shifts in the yield curve. Ng considers two different strategies:

Strategy 1: Immunization of the single liabilities using zero-coupon bonds held to maturity

Strategy 2: Immunization of the single liabilities using coupon-bearing bonds while continuously matching duration.

The effects of a non-parallel shift in the yield curve on Strategy 2 can be reduced by:

选项:

A.

minimizing the convexity of the bond portfolio.

B.

maximizing the cash flow yield of the bond portfolio.

C.

minimizing the difference between liability duration and bond-portfolio duration.

解释:

A is correct.

Minimizing the convexity of the bond portfolio minimizes the dispersion of the bond portfolio. A non-parallel shift in the yield curve may result in changes in the bond portfolio’s cash flow yield. In summary, the characteristics of a bond portfolio structured to immunize a single liability are that it (1) has an initial market value that equals or exceeds the present value of the liability, (2) has a portfolio Macaulay duration that matches the liability’s due date, and (3) minimizes the portfolio convexity statistic.

我感觉这个题和答案有点奇怪啊,non-parallel shift 造成的是structural risk,应该用zero-coupon bond来解决。

convexity和non-parallel分别是造成 immunization risk的两个原因呀,感觉这三个选项都不对啊

1 个答案

发亮_品职助教 · 2020年02月06日

嗨,努力学习的PZer你好:


“non-parallel shift 造成的是structural risk,应该用zero-coupon bond来解决。”


用Zero-coupon bond来匹配单期负债,的确是最完美的匹配,他是没有任何匹配风险的。

当我们无法在市场上找到合适的Zero-coupon bond来匹配负债时,我们就只能构建一个附息债券Bond portfolio来匹配单期负债。

所以,非平行移动时,用附息债券组合来匹配单期负债,多多少少都是有Structural risk的,即非平行移动时,资产与负债不匹配的风险。

为了尽可能地降低Structural risk,我们就想办法让附息债券组合的表现足够地像零息债券的表现,这样我们就仿佛再用零息债券匹配单期负债一样。



如何让附息债券组合的表现足够地像零息债券?


零息债券最大的特点,就是只有到期一笔现金流,那构建债券Portfolio来匹配单期负债,我们就让附息债券组合的现金流足够地集中在负债到期日附近,附息债券的现金流越集中,就好像附息债券的现金流就只发生在负债到期日这天,这就仿佛再用零息债券匹配负债一样。

因为零息债券匹配是完美、无风险的,所以用附息债券组合匹配时,越是像零息债券,Structural risk就越小。

所以,只要我们让附息债券组合的现金流足够地集中,就能尽可能地降低非平行移动时,资产不匹配负债的风险。

债券的现金流越集中,反映出来的债券Convexity数据越小;同时,附息债券组合的现金流足够地集中,匹配时Structural risk就越小;

所以我们可以总结为:匹配时,债券资产的Convexity数据越小,非平行移动时面临的Structural risk就越小。



所以这道题的题目问:对Strategy 2做什么样的条件,可以降低非平行移动时产生的影响?

从上面的分析中可以知道,我们要尽可能地降低匹配资产的Convexity数据,就能尽可能地降低Structural risk,于是选A。



“convexity和non-parallel分别是造成 immunization risk的两个原因呀”


在其他教材(包括18年以前的CFA教材)里确实有Non-parallel shift会造成Immunization risk;

但现在在咱们3级的最新教材里,平行移动,与绝大多数非平行移动,匹配都是可以成功的。保证成功的条件就是尽可能地降低资产的Convexity数据。

刚刚回答了一个Structural risk与Convexity的问题,可以参考:http://class.pzacademy.com/qa/questions/48028

有问题可以继续追问~


-------------------------------
努力的时光都是限量版,加油!


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